| Summary: | <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="italic">Background</mi><mo>:</mo></mrow></semantics></math></inline-formula> End-stage renal disease patients undergoing hemodialysis (ESRD-HD) therapy are highly susceptible to malignant ventricular arrhythmias caused by undetected potassium concentration ([<inline-formula><math display="inline"><semantics><msup><mi>K</mi><mo>+</mo></msup></semantics></math></inline-formula>]) variations (<inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula>) out of normal ranges. Therefore, a reliable method for continuous, noninvasive monitoring of [<inline-formula><math display="inline"><semantics><msup><mi>K</mi><mo>+</mo></msup></semantics></math></inline-formula>] is crucial. The morphology of the T-wave in the electrocardiogram (ECG) reflects <inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula> and two time-warping-based T-wave morphological parameters, <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mi>w</mi></msub></semantics></math></inline-formula> and its heart-rate corrected version <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mrow><mi>w</mi><mo>,</mo><mi>c</mi></mrow></msub></semantics></math></inline-formula>, have been shown to reliably track <inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula> from the ECG. The aim of this study is to derive polynomial models relating <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mi>w</mi></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mrow><mi>w</mi><mo>,</mo><mi>c</mi></mrow></msub></semantics></math></inline-formula> with <inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula>, and to test their ability to reliably sense and quantify <inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula> values. <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="italic">Methods</mi><mo>:</mo></mrow></semantics></math></inline-formula> 48-hour Holter ECGs and [<inline-formula><math display="inline"><semantics><msup><mi>K</mi><mo>+</mo></msup></semantics></math></inline-formula>] values from six blood samples were collected from 29 ESRD-HD patients. For every patient, <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mi>w</mi></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mrow><mi>w</mi><mo>,</mo><mi>c</mi></mrow></msub></semantics></math></inline-formula> were computed, and linear, quadratic, and cubic fitting models were derived from them. Then, Spearman’s (<inline-formula><math display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>) and Pearson’s (<i>r</i>) correlation coefficients, and the estimation error (<inline-formula><math display="inline"><semantics><msub><mi>e</mi><mi>d</mi></msub></semantics></math></inline-formula>) between <inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula> and the corresponding model-estimated values (<inline-formula><math display="inline"><semantics><mrow><mover accent="true"><mi>Δ</mi><mo>^</mo></mover><mrow><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></mrow></semantics></math></inline-formula>) were calculated. <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="italic">Results and Discussions</mi><mo>:</mo></mrow></semantics></math></inline-formula> Nonlinear models were the most suitable for <inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula> estimation, rendering higher Pearson’s correlation (median 0.77 <inline-formula><math display="inline"><semantics><mrow><mo>≤</mo><mi>r</mi><mo>≤</mo></mrow></semantics></math></inline-formula> 0.92) and smaller estimation error (median 0.20 <inline-formula><math display="inline"><semantics><mrow><mo>≤</mo><msub><mi>e</mi><mi>d</mi></msub><mo>≤</mo></mrow></semantics></math></inline-formula> 0.43) than the linear model (median 0.76 <inline-formula><math display="inline"><semantics><mrow><mo>≤</mo><mi>r</mi><mo>≤</mo></mrow></semantics></math></inline-formula> 0.86 and 0.30 <inline-formula><math display="inline"><semantics><mrow><mo>≤</mo><msub><mi>e</mi><mi>d</mi></msub><mo>≤</mo></mrow></semantics></math></inline-formula> 0.40), even if similar Spearman’s <inline-formula><math display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> were found across models (median 0.77 <inline-formula><math display="inline"><semantics><mrow><mo>≤</mo><mi>ρ</mi><mo>≤</mo></mrow></semantics></math></inline-formula> 0.83). <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="italic">Conclusion</mi><mo>:</mo></mrow></semantics></math></inline-formula> Results support the use of nonlinear T-wave-based models as <inline-formula><math display="inline"><semantics><mrow><mi>Δ</mi><mo>[</mo><msup><mi>K</mi><mo>+</mo></msup><mo>]</mo></mrow></semantics></math></inline-formula> sensors in ESRD-HD patients.
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